Non-Cartesian 3D-SPARKLING vs Cartesian 3D-EPI encoding schemes for functional Magnetic Resonance Imaging at 7 Tesla

The quest for higher spatial and/or temporal resolution in functional MRI (fMRI) while preserving a sufficient temporal signal-to-noise ratio (tSNR) has generated a tremendous amount of methodological contributions in the last decade ranging from Cartesian vs. non-Cartesian readouts, 2D vs. 3D acquisition strategies, parallel imaging and/or compressed sensing (CS) accelerations and simultaneous multi-slice acquisitions to cite a few. In this paper, we investigate the use of a finely tuned version of 3D-SPARKLING. This is a non-Cartesian CS-based acquisition technique for high spatial resolution whole-brain fMRI. We compare it to state-of-the-art Cartesian 3D-EPI during both a retinotopic mapping paradigm and resting-state acquisitions at 1mm3 (isotropic spatial resolution). This study involves six healthy volunteers and both acquisition sequences were run on each individual in a randomly-balanced order across subjects. The performances of both acquisition techniques are compared to each other in regards to tSNR, sensitivity to the BOLD effect and spatial specificity. Our findings reveal that 3D-SPARKLING has a higher tSNR than 3D-EPI, an improved sensitivity to detect the BOLD contrast in the gray matter, and an improved spatial specificity. Compared to 3D-EPI, 3D-SPARKLING yields, on average, 7% more activated voxels in the gray matter relative to the total number of activated voxels.

Second, and specifically regarding the distributions of the residuals, we compared the results associated with 3D-SPARKLING to those associated with 3D-EPI and corresponding to the same volunteer (V#3).
Figure 10(A) shows the maps of the voxel-wise difference of the β coefficients derived from the baseline regressor in the GLM and associated with 3D-SPARKLING data reconstructed using (a) to (c): After computing the β coefficient maps associated with the baseline regressor and each reconstruction strategy ((a) to (c)), the voxel-wise that the bias induced by the nonlinearity (β ℓ1 − β ℓ2 ) is actually lower than that induced by the regularization (β ℓ1 − β noregu or β ℓ2 − β noregu ).In Figure 10(B), the histograms of these voxel-wise differences in β coefficients are plotted and confirm the above observations: As the distribution of these differences is narrower or tighter between the two regularized (linear versus nonlinear) reconstruction strategies as compared to the differences between the regularized and unregularized strategies, most of the bias is due to the regularization itself and not to its nonlinear aspect.differences between these maps were computed, namely, β ℓ1 − β ℓ2 , β ℓ1 − β noregu and β ℓ2 − β noregu .There are visible differences between the 3 maps.As we assume that reconstruction strategy (c) yields no bias as it's not regularized, these results suggest Figure 11(A) shows the residual error maps associated with 3D-SPARKLING (reconstructed using (a)-(c) strategies) and 3D-EPI fMRI volumes.These maps were produced by averaging the temporal residual errors over the time dimension to obtain a global summary.The residual error seems centered around zero for the four datasets.Additionally, reconstruction strategy (c) results in more lost signal than (a) and (b) as the residuals reach higher values.Figure 11(B) shows the histograms of the temporal residual error of the GLM-fitted fMRI volumes: Firstly, we spatially averaged the residual errors over the brain mask, then computed the temporal histograms1 .The results associated with the four scenarios, namely the data acquired with 3D-SPARKLING and reconstructed using strategies (a)-(c) and those acquired with 3D-EPI, are reasonably similar.Despite small differences between the histograms associated with the reconstruction strategies (a)-(c), the distributions are centered around zero.Furthermore, the histograms associated with 3D-SPARKLING and reconstruction strategy (a) and that associated with 3D-EPI are quite similar and are spread alike around zero.Additionally, to obtain an objective measure of the similarity between these histograms and evaluate how tenable the hypothesis of the Gaussianity of the residuals is, a Kolmogorov-Smirnov (KS) test was performed between: (i) The histograms associated with 3D-SPARKLING data and reconstruction strategies (a) and (b), respectively.
(ii) The histograms associated with 3D-SPARKLING data and reconstruction strategies (a) and (c), respectively.
(iii) The histograms associated with 3D-SPARKLING data and reconstructed using (a) and those associated with 3D-EPI.
The null hypothesis (H 0 ) used is that the two distributions are identical and the p-values were, 0.18, 0.1, and 0.9 for (i), (ii), and (iii), respectively.This means that H 0 cannot be rejected and therefore that the distributions are significantly similar.We conclude that the hypothesis of Gaussianity remains tenable for 3D-SPARKLING data reconstructed with a CS-based reconstruction.This could be explained by the fact that the level of regularization performed was set to a reasonably good but low value.

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Fig 10. (A): Maps of the voxel-wise difference between the β coefficients derived from the baseline regressor in GLM analysis and associated with 3D-SPARKLING data reconstructed using (a) to (c) in V#3.(B): Histograms of these maps.

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Fig 11. (A) Maps and (B) temporal histograms of the residual error of the GLM-fitted retinotopic fMRI data associated with 3D-SPARKLING (reconstructed with strategies (a)-(c)) and 3D-EPI and collected in V#3.